The rapid increase in lithium-ion batteries (LIBs) usage, particularly in portable electronics and electric vehicles, has led to considerable environmental challenges due to waste generation, creating a need for recovery of metals from waste. This review examines methods for recovering valuable metals—Co, Ni, Mn, and Li—from the leachates of end-of-life spent LIBs using hydrometallurgical unit processes, summarizing current research and technological advancements. Recovery techniques such as precipitation, solvent extraction, electrodeposition, ion exchange (and adsorption), and other approaches were evaluated in terms of efficiency, cost-effectiveness, and environmental impact. Moreover, a cost analysis comparing hydrometallurgical methods—precipitation, solvent extraction, electrochemical extraction—was conducted. This review highlights the technological gaps in current recovery methods and stresses the need for further research to improve metal recoveries and minimize the environmental impacts of hydrometallurgical processes. Integrating experimental findings, the review offers a comprehensive overview of recovery pathways and provides insights into the future of sustainable LIBs recycling and cost analysis.